Static electric polarizability dipole

The static electric dipole polarizability a of the model system investigated is therefore... 

TOO Schwerdtfeger, P. (2006) Atomic Static Dipole Polarizabilities, in Computational Aspects of Electric Polarizability Calculations Atoms, Molecules and Clusters (ed. G. Maroulis), Imperial College Press, London, pp. 1-32. 

Formal Theory A small neutral particle at equilibrium in a static electric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vector and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = auE, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

To obtain a clear understanding of electrodynamic bonding, start with the field of a static electric dipole. Then, let the dipole oscillate so it emits electromagnetic waves (photons). Consider what happens when the emitted field envelopes another dipole (London, 1937). Finally, determine the factors that convert neutral molecules into dipoles (that is, their polarizabilities). 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

We have performed a series of semiempirical quantum-mechanical calculations of the molecular hyperpolarzabilities using two different schemes the finite-field (FF), and the sum-over-state (SOS) methods. Under the FF method, the molecular ground state dipole moment fJ.g is calculated in the presence of a static electric field E. The tensor components of the molecular polarizability a and hyperpolarizability / are subsequently calculated by taking the appropriate first and second (finite-difference) derivatives of the ground state dipole moment with respect to the static field and using... 

In this way, the relative dielectric response to static electric fields of a gas of polarizable molecules that also bear a permanent dipole moment is... 

This polarization has two components the induced polarization P (due to movement of the centers of charge, or to the static electric dipole polarizability a of molecules) and the dipole polarization Pjt (due to the orientation of the permanent dipoles m in the applied electric field E) ... 

Let us now consider the second-order molecular properties. The static electric dipole-polarizability tensor is given by the expression... 

The calculation of the molar polarizabilities, often involves statistical mechanical averaging over orientational distributions of the molecules. An important example is the distribution function w caused by dipole orientation in an externally applied static electric field E° because it describes the process of electric poling of NLO-phores. To second order in the field, the dipolar contributions to this (normalized) function are given by (100),... 

It must be stressed that the polarizability gradient da/dQk also appears in the equation for Raman intensities [175], as indicated also by Lambert [176]. Thus, in view of Eq. (25), we can extend the consequences of the static electric field to vibrations which are forbidden by the surface selection rule the high electric field in the double layer can induce a dipole moment component in the direction of the field on permanent dipoles which are parallel to the surface. Thus the effect of orientation due to the electric field is just a manifestation of the Stark effect. 

The molecular response tensors are characterized by peculiar properties and satisfy a series of very general quantum-mechanical relations. First we observe that the dynamic properties can be rewritten as a sum of the corresponding static property and a function multiplying the square of the angular frequency. Thus, for instance, in the case of dipole electric polarizability, using Eqn. (117),... 

Table 1. First and second ionization potentials /, and /j (in eV) and static electric dipole polarizabilities a (in A ) for noble gas elements and first-row atoms...

Polarizability (i.e., static dielectric polarizability), a, is a measnre of the linear response of the electronic clond of a chemical species to a weak external electric field of strength E. For isotropic molecnles, the dipole moment, fi, is... 

To calculate the static linear polarizability one has to compute first the total dipole moment (by fixed geometry) at different trial electric field strengths Ej (six were applied). The dipole moments as a function of the different Ets were fitted to a polynomial expansion in the components of Ej. From the coefficients of this expansions it is easy to obtain the static polarizabilities on the basis of the... 

The terms that are nonlinear in a arise because the state wavefunction 0> depends on a (i.e., the state has responded to a//, which gives rise to the name response property"). When, for example, a// j represents a static electric field (a//, = 6 r), Ej yields the permanent electric dipole moment (/i) of the unperturbed state 0>, Ej gives this stale s polarizability (oc), and E, E4, etc. yield successively higher hyperpolarizabilities (/i,y, etc.). 

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